Euclidean Embeddings of Snowflake Metric Spaces

Metric spaces are useful tools for modeling sets of objects where there is a natural notion of distance; examples include geographical data, genetic data, and signals (like sound waves or images). We often seek to classify metric spaces by how Euclidean they look: specifically, we want to know if some metric space can be embedded in Euclidean space. In this talk we will use examples to introduce the general embedding problem. We will then discuss a theorem by Assouad guaranteeing bi-Lipschitz embeddings of so-called snowflake metric spaces into Euclidean space and some related work by Naor-Nieman and David-Snipes.